Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk

Authors:
HONGZHAO LIN

Abstract:
The reducing subspaces of
Toeplitz operators $T_{z_1^N}$(or $T_{z_2^N}$), $T_{z_1^Nz_2^N}$, and $T_{z_1^Nz_2^M}$ on Dirichlet type spaces of the bidisk ${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$ are described, which extends the results for the corresponding operators on the Bergman space of the bidisk.